


Strange Attractors

by kusuriurikun



Series: Shibuya Continuum [2]
Category: Subarashiki Kono Sekai | The World Ends With You
Genre: Character Study, Drabble, Gen, Math and Science Metaphors, Mathematics, Observations on Shibuya, POV Antagonist, Platonic Relationships, Pre-Canon
Language: English
Status: Completed
Published: 2020-08-15
Updated: 2020-08-15
Packaged: 2021-03-06 07:27:05
Rating: General Audiences
Warnings: No Archive Warnings Apply
Chapters: 2
Words: 1,427
Publisher: archiveofourown.org
Story URL: https://archiveofourown.org/works/25919554
Author URL: https://archiveofourown.org/users/kusuriurikun/pseuds/kusuriurikun
Summary: Musings on chaotic functions just before the beginning of the work day by a certain Sho Minamimoto.  Just before the events of TWEWY proper.One of an ever-increasing set of looks into Sho's life and mind.As per usual, due to some fairly heavy use of mathematical terms an author's note is included at the end.
Series: Shibuya Continuum [2]
Series URL: https://archiveofourown.org/series/1902298
Comments: 2
Kudos: 8





	1. On the nature of Shibuya as a function

Sho Minamimoto sits on one of his trash-heaps, like some feral heavy-metal Rodin art piece, at way too early in the AM observing the city as he tends to do...and in these times, the few times where his head is not full of reverb and static from the background count of Shibuya and its throngs...he comes to a bit of a realisation.

As night turns to day at dawn in nature’s own boundary transition, Sho ponders on other boundary conditions and the interesting things that happen at them.

He’d seen those areas where the RG and UG met, where Player and Reaper and the living meet as crossover points in a function; he muses now that in the chaos that is this town, this district...the places of crossover are strange attractors of a sort, pulling functions to them.

The Scramble Crossing itself, obviously, being a zero point of this whole exercise, its own basin of attraction as the dead binomials find themselves as randomness seeds in that grand function of the Game.

The various couture shops which were their own basins of attraction as the monomials lived to shop and the binomials shopped to live.

Old man Doi’s Ramen Don, which was its own attraction basin for the kids on a mission (to live, to get the latest Tin Pin news, to wind down after school--the variables always were different) and the salarymen getting off way too late from work and every iteration in between.

The Dead God’s Pad, which was its own basin for those like himself bound as complex functions bound and yet seeking to escape to infinity.

The WildKat Cafe, its own especially complex orbit, which always seemed to be open at exactly the right time, but (as in the manner of functions of this type) was never exactly the same time every day, but depended on the sensitive initial condition of the day of its owner.

The CAT mural in and of itself, a grand sink of attraction in both the real and the imaginary, and a powerful source of chaos from the latter to the former.

* * *

The polynomials of the UG, Sho muses, could _also_ be strange attractors in their own right.

Megs tended to be an attractor for those like himself--the complex functions that hung out at the edge of not quite escaping to infinity and not quite decaying to zero but hanging out on the border line.

Really, _all_ the Officers were strange attractors of a sort. 

Sho’s thoughts turn to Ol’ Ram-Crotch, the new function in the set. (Sho remembered Ram-Crotch from life; he’d been a short-order chef who left about a year before The Accident to--as it turned out--start his own place, had his own misadventure landing him in the UG, and now was Competition, though his own basin of attraction was not wanting to be an understudy.)

Her Iron Frostiness was one too, of a sort, and a definite Threat. {Her basin of attraction was power and dominance. Honestly Sho considered her best avoided.)

Even the occasional monomial turns out to be a strange attractor, he muses. Eiji F’ing Oji (literally), who is in his own way a basin of attraction for the living based on his own seed of his ego and a popular blog.

And then there’s Sanae Hanekoma, who’s a veritable walking example of the Lorenz attractor in and of himself. A living (as much as anyone lives in the UG), breathing ( _ibid._ ) chaotic system all its own.

Since Sho found himself pulled to _that_ particular attractor, he’s seen a little more of how much of the UG works--and, occasionally, doesn’t work. How the Composer is the source of the initial set and function, and that the system is stuck in the bland stasis of the non-chaotic sections of a fractal outside (or inside) of its Hausdorff dimension, and how a new randomness seed is needed.

Hanekoma’s flat out _admitted_ to Sho that he’s actually been generating attractors. The Mural is a function designed to be a perturbation specifically leading to an axiom of choice, though (as with all chaotic functions) the actual path of the function never goes _quite_ the same for every variable.

And really, Sho thinks, that’s the beauty in chaos and mathematics. A simple equation can make something so _complex_ and give it life--make it _evolve_. A butterfly flapping its wings in Florida can spawn a typhoon a week later in Okinawa. A map of the chaotic function of the weather itself looks a bit like the wings of a butterfly, like God’s own personal easter egg in the code of reality.

When Sho is Composer, he’s gonna do some _zetta_ perturbation of this set. By the time he’s done, all of Shibuya will be a strange attractor as interconnected and infinite in its complexity as the Mandelbrot set. 

When he ends up on top and the present management ends up on bottom the charm and beauty and inner truth of this place is going to be writ large in the strange like an elegant function.

That function hasn’t gone through its iterations just yet, but it’s just a function of time.

Sho looks down at the yoctograms looking up their mission for the day and in chaos finds inspiration.

Time to make them show him their beauty. This was gonna be _zetta_ fun.


	2. Appendix: Author's notes and terminology

A few notes on the mathematical references for those who are  _ not  _ the sort who had their noses in books on chaos theory at age 18:

The Rodin reference is to [_The Thinker_](https://en.wikipedia.org/wiki/The_Thinker) specifically, a quite famous sculpture (with around 28 castings, give or take); this is a bit of intentional play with [this bit of official art of Sho on one of his trash-henges](https://twewy.fandom.com/wiki/Sho_Minamimoto/Gallery?file=Minamimoto.png). 

A  [ strange attractor ](https://en.wikipedia.org/wiki/Attractor#Strange_attractor) is, well, a mathematical attractor that tends to be a “convergence point” for a chaotic dynamic system. These tend to be the points at which the most “interesting” parts of a mapping of a chaotic system happen--specifically in the basins of attraction that tend to be the “convergence seeds” of a function. (This is the area in maps of chaotic functions where you tend to see the nifty fractal stuff--most notably in  [ Newton fractals ](https://en.wikipedia.org/wiki/Newton_fractal) .) 

Likewise, a “ [ Hausdorff dimension ](https://en.wikipedia.org/wiki/Hausdorff_dimension) ” is essentially a way of saying “how actually  _ fractal  _ a fractal  _ is _ ”; Sierpinski triangles, for instance, have a Hausdorff dimension of ln(3)/ln(2) ≈ 1.58.

(And before anyone asks: No, you can’t actually have an object with a Hausdorff dimension of  _ pi _ , not without playing with hypercubes and other fun higher-than-3d constructs.)

The  [ Lorentz attractor ](https://en.wikipedia.org/wiki/Lorenz_system) is probably one of the most famous examples of a fractal centered around a strange attractor, and was arguably one of the first strange attractors described in a paper on a chaotic system; it also is a mathematical explanation of (among other things) why weather forecasting other than general climatic trends is pretty much  _ impossible _ more than a few days in advance. The classical graph does resemble a butterfly’s wings, and the actual implications of the Lorenz system (and the rather unique and attractive graph) inspired the term of the “ [ butterfly effect ](https://en.wikipedia.org/wiki/Butterfly_effect) ”.

Yes, there is a horrible physics pun involving the  [ six types of quarks ](https://en.wikipedia.org/wiki/Quark) which I couldn’t resist (especially in light of, well, essentially rewriting the UG and Sho's minor secondary fascination with the speed of light and certain SI units).

And--just for the record--I am still, to this day, impressed that  _ The World Ends With You  _ essentially predicted the rise of Instagram social influencers. (And Internet memes meant as tools of social influence, but that’s another story. At least we're all aware on how to imprint a meme now! :D)

* * *

This particular drabble came to me at literally oh-god-too-early-thirty AM, and pretty much it would Not Stop--in a way, writing about Sho’s thoughts has become a strange attractor in and of _itself_ (and one for what turns out to be a rather  _ complex _ fractal of an individual indeed, the math jokes aside). This has been a perturbation, yes, but in a  _ good _ way, and really it’s pushed me out of my usual comfort zone into exploring a creative medium I haven’t done much with previously.

Something tells me a certain artist-barista in a cafe with whenever-the-fuck-I-feel-like-it hours would approve. :3  


1021 (9x+7i>3(3x-7u)) for values of u=∀ ( as a certain feral mathgeek would say)--or, reduced,  _ I zetta <3 all of you  _ for actually reading this and your kind comments on my previous fic.


End file.
